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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 8880p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8880.c1 | 8880p1 | \([0, -1, 0, -1861, -58439]\) | \(-2785840267264/4273846875\) | \(-1094104800000\) | \([]\) | \(12960\) | \(1.0016\) | \(\Gamma_0(N)\)-optimal |
8880.c2 | 8880p2 | \([0, -1, 0, 15899, 1182985]\) | \(1736064508952576/3387451171875\) | \(-867187500000000\) | \([]\) | \(38880\) | \(1.5509\) |
Rank
sage: E.rank()
The elliptic curves in class 8880p have rank \(1\).
Complex multiplication
The elliptic curves in class 8880p do not have complex multiplication.Modular form 8880.2.a.p
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.